Molar volume, mean partial

Consider Ni exposed to Oj/HjO vapour mixtures. Possible oxidation products are NiO and Ni (OH)2, but the large molar volume of Ni (OH)2, (24 cm compared with that of Ni, 6.6 cm ) means that the hydroxide is not likely to form as a continuous film. From thermodynamic data, Ni (OH)2 is the stable species in pure water vapour, and in all Oj/HjO vapour mixtures in which O2 is present in measurable quantities, and certainly if the partial pressure of O2 is greater than the dissociation pressure of NiO. But the actual reaction product is determined by kinetics, not by thermodynamics, and because the mechanism of hydroxide formation is more complex than oxide formation, Ni (OH)2 is only expected to form in the later stages of the oxidation at the NiO/gas interface. As it does so, cation vacancies are formed in the oxide according to... 

In many instances it is possible to determine the partial molar volumes of binary systems by graphical means. Some cases simply require the application of calculus to the equations developed. As an example we consider Equations (6.57) and (6.58). We plot 4>V against m, determine the slope of the curve at a given m, and then determine Vx and V2 by means of these equations. 

Fig. 1.3. Partial molar volume (a) the molar volume v,° of a pure substance i and the partial molar volume v, of substance i in a homogeneous mixture (b) graphical determination of the partial molar volumes of constituent substances in a homogeneous binary system by the Bakhuis-Rooseboom Method v = V/(n, + nt) = the mean molar volume of a binary mixture x2= the molar fraction of substance 2 Vj = v - x2(dv/dx2) = the partial molar volume of substance 1 v2 = v-(l-x2 avldx2) = the partial molar volume of substance 2. [Ref. 1.]...

Figure 4.7 shows the population ratios of Wc5/Wpn, WapL/Wpn, Wap/ Wpu, and WaL/Wpu as functions of pressure V at the constant temperature of T = 298 K. As pressure increases, both IVc6/Wpn and Wap/Wpu decrease, although the WaR/Wpu and Waij/Wpn data have too large error bars to discuss their pressure dependence. The increase in pressure at constant temperature generally causes the decrease in volume. The decreases in Wcs/Wpu and Wap/Wpu means that the volumes of the C5 and ap states are larger than that of the Pn. The difference of partial molar volume AV of the C5 state from that of the Pn state is, for instance, calculated from the derivative of Wc6/IVpn with respect to pressure V by... 

We are concerned in this experiment with the partial molar volume Vj, which may be thought of as the increase in the volume of an infinite amount of solution (or an amount so large that insignificant concentration change will result) when 1 mole of component i is added. This is by no means necessarily equal to the volume of 1 mol of pure i. 

The magnitude of the fluctuations in volume (dilatation) and density (condensation) associated with US wave is controlled by the properties of the medium and the applied forces. The velocity of sound in mixtures and suspensions will therefore be controlled by the mean density and mean compressibility as expressed by the Urick equation (see Eq.9.7-9.10). The equation can be formulated in terms of partial molar volumes by forming an identity between the volume fraction of the solute, its partial volume Vm2), the mean molar volume of the solution Vm) and the mole fraction Cm) as follows ... 

The partial molal volume of the constituent i in a mixture of ideal gaseSf which do not react, is equal to its molar volume Vi in the system, since there is no volume change on mixing if p, is the partial pressure of the constituent, then Vi is equal to RTfpi, where R is the gas constant per mole and T is the absolute temperature. It can be shown by means of thermodynamics that the partial molal volume (Vi) is related to the chemical potential by the equation... 

This provides a means of finding the partial molal volumes as illustrated in Fig. 1.19.1, one measures the molar volume of the solution at a set of X2 values. At the particular value X2 = b a tangent to the curve is drawn. The points of intersection of this tangent at X2 = 0, 1 yields the desired quantities Vi and V2 respectively. 

Just as for all ideal systems (c/. 7.20 and 7.21), the partial molar enthalpies and the partial molar volumes of perfect or ideal solutions are dependent only on T and p. We then have for the mean molar enthalpy and volume... 

Hiis condensation or contraction is the cause of the highly negative partial molar volumes, which become more pronounced as the isothermal compressibility increases. These clusters are bound by van der Waals forces and are thus very different from other types of aggregates such as clathrates which are bound by specific chemical forces. Their size can reach values on the order of 100 molecules, which means that they extend over many coordination shells. While the partial molar volume, a macroscopic property, provides evidence of clustering, more detailed information has been obtained recently using spectroscopic techniques which probe solute-solvent interactions directly. 

D is correct. You should know that 1 atm is equal to 760 torr. Since the partial pressure of nitrogen is 600, the mole fraction of nitrogen is 0.79. This means that the percentages given are by particle and not by mass. D would be true if the percentages were based on mass. If you chose B, you need to go back to Lecture 3 and review standard molar volume. 

Another asp>ect of partial molar volumes and heat contents, in particular, arises from the thermod3mamic requirement that for an ideal gas mixture or for an ideal liquid solution, as defined for example in 30a and 34a, respectively, there is no change of volume or of heat content upon mixing the components. This means that the partial molar volume and heat content of each substance in the mixture are equal to the respective molar values for the pure constituents. Any deviation of the partial molar quantity from the molar value then gives an indication of departure from ideal behavior this information is useful in connection with the study of solutions. 

In general, this approach may be used in the evaluation of those properties for which the ideal behavior of the system is physically defined, e.g. for Gibbs energy of mixing and the molar volume. The procedure can be demonstrated by means of the calculation of equilibrium composition based on the measurement of density in the system A-B in which the intermediate compound AB is formed. The compound AB undergoes at melting a partial thermal dissociation. 

This equation, which is one example of the Gibbs-Duhem equation, shows that changes in the partial molar volume of one component may be related to changes in the same quantity for the other component. Experimentally, it means that one only has to measure one partial molar volume as a function of composition provided one has a value of the second partial molar volume at a reference point. In order to illustrate this point, equation (1.4.8) is written in a form suitable for calculating ua from ug ... 

Water is unique among polar solvents in that it is a small molecule with a low molar volume. As a result, the concentration of water in pure water is 55.5 M. This means that the mole fraction of water in dilute aqueous solutions is close to one, and the partial molar quantities in these solutions are close to the corresponding quantities for the pure solvent. Other solvents have considerably higher molar volumes, and therefore, lower concentrations in the pure solvent. The... 

Table 6.10 shows that the partial molar volumes and particularly the isentropic partial molar compressibilities at infinite dilution are significantly higher in the micellar environment than in water. As far as the partial molar volume is concerned, the increment per CH2 group is reasonably constant. The values are 15.9 cmVmol in water and 16.8 cmVmol in the micelles. This can be compared to a CH2 group value of 16.1 in octane and 16.2 in heptane and 16.8 for the molar volume of pure alcohols. It means that as far as the volume of a CH2 group in the micelle is concerned, pure alcohol is the best comparison. 

Let us consider the application of transition state analysis to interpret the work of Ehrlich and coworkers on the reaction behavior of ethylene polymerization in supercritical ethylene (Ehrlich, 1971). Ehrlich presents experimental data on the polymerization of ethylene at 130°C and 1,500 bar. At these conditions supercritical ethylene can solubilize 5 wt% to 10 wt% high molecular weight polyethylene, which is produced during the reaction. Normally, the conversions are kept to —10% which means that the reacting supercritical ethylene-polyethylene mixture is near a mixture critical point. Ehrlich argues that the partial molar volume of M, which has volumetric... 

At high pressures, the meaning of < il is not as clear as at low pressure. However, the use of a single equation of state for both liquid and gas mixtures has clear advantages over the conventional method, where activity coefficients, the gas-phase equation of state, and liquid partial molar volumes are required as a function of temperature (and pressure). 

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